1. Field
The following pertains to the fields of information storage and transfer, and more particularly to the field of retrieving information from an inter-symbol interference (ISI) channel.
2. Description of Related Art
A “channel” is a term for a model of any system that conveys information through space and/or time, e.g., storage media and communication systems can be modeled as channels.
An ISI channel refers to a type of distortion channel. Distortion refers to temporal spreading and consequent overlap of individual pulses to the degree that a receiver cannot reliably distinguish between individual signal elements. For example, a partial response magnetic recording channel is an ISI channel. The wireless fading channel, usually modeled as a tapped-delay-line is also an ISI channel.
Every channel has a capacity. As long as the transmission rate is less than the channel capacity, it is possible to obtain a low-error rate system through the use of certain error correction codes. LDPC codes are known examples of good performance error correction that allow transmission rates close to channel capacity at achievable signal-to-noise ratios (SNR).
LDPC codes are linear block codes that have parity check matrixes with a small number of nonzero elements in each row and column. LDPC codes can be constructed over any Galois Field. For example, a binary LDPC code is defined over GF(2), in which “1” is the only nonzero element. Since LDPC codes are block codes, it is necessary to receive a whole codeword before the LDPC decoding process can begin.
LDPC decoders use soft information during decoding. Soft information can be generated by a soft information detector, such as the Soft Output Viterbi Algorithm (SOVA) or the Bahl Cocke Jelinek Raviv (BCJR) algorithm.
Decoders for ISI channels can use a soft information detector followed by an LDPC decoder in an iterative fashion. As data rates and/or densities continue to increase, LDPC decoders should perform well in lower signal to noise (SNR) situations.